a+4a-14+7+1/2a=180

Solution for a+4a-14+7+1/2a=180 equation:

a+4a-14+7+1/2a=180

We move all terms to the left:

a+4a-14+7+1/2a-(180)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

5a+1/2a-187=0

We multiply all the terms by the denominator


5a*2a-187*2a+1=0

Wy multiply elements

10a^2-374a+1=0

a = 10; b = -374; c = +1;
Δ = b2-4ac
Δ = -3742-4·10·1
Δ = 139836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{139836}=\sqrt{4*34959}=\sqrt{4}*\sqrt{34959}=2\sqrt{34959}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-374)-2\sqrt{34959}}{2*10}=\frac{374-2\sqrt{34959}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-374)+2\sqrt{34959}}{2*10}=\frac{374+2\sqrt{34959}}{20}
$